Vortex-Repartition in the Two-Dimensional Ginzburg-Landau Model with Magnetic Field

I will present some results obtained jointly with Etienne Sandier on the Ginzburg-Landau model of superconductivity in 2 dimensions, and partly described in our recent book. In a superconducting sample, according to the intensity of the applied field, phase transitions happen and vortices appear in certain regimes. By studying energy minimizers in a suitable parameter regime, we extract limiting problems that describe the optimal repartition of vortices according to the applied field.